Premium
Shedding new light on Hierarchical Principal Component Analysis
Author(s) -
Hanafi Mohamed,
Kohler Achim,
Qannari El Mostafa
Publication year - 2010
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1334
Subject(s) - principal component analysis , block (permutation group theory) , convergence (economics) , computer science , monotonic function , computation , component analysis , algorithm , multivariate statistics , component (thermodynamics) , relation (database) , mathematical optimization , mathematics , data mining , artificial intelligence , machine learning , mathematical analysis , physics , geometry , economics , thermodynamics , economic growth
Hierarchical Principal Component Analysis (HPCA) is a multiblock method which is designed to reveal covariant patterns between and within several multivariate datasets. The computation of the parameters of this method, namely block scores, block loadings, global loadings and global scores, is based on an iterative procedure. However, very few properties are known regarding the convergence of this iterative procedure. The paper discloses a monotony property of HPCA and exhibits an optimization criterion for which HPCA algorithm provides a monotonic convergent solution. This makes it possible to shed a new light on this method of analysis by showing new properties and pinpointing its relation to existing methods such as Common Component and Specific Weights Analysis (CCSWA), INDSCAL and PARAFAC Models. Copyright © 2010 John Wiley & Sons, Ltd.